Fuzzy Value‐at‐risk: Accounting for Market Liquidity

Abstract

In this paper we present a value‐at‐risk measure which accounts for market liquidity. We show that taking into account market liquidity implies a decoupling of valuation of long and short positions. We present a pricing model, named fuzzy measure model, that yields different values for positions of different sign and that can be usefully exploited to account for liquidity risk. This methodology is well‐suited to price options when the distribution of the underlying asset is not known precisely, as in the case of implied options in corporate claims or real options. As an example, we apply our pricing technique to an option based model of value‐at‐risk, in line with the Merton and Perold approach, and we recover different value‐at‐risk figures for long and short positions.(J.E.L.: C00, D81, G12).